082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

266 Chapter 8 Matrix algebra
4
5
6
⎛ ⎞ ⎛ ⎞
71723 81617
⎝−1 10 19⎠,
⎝17 4 8⎠
2410 4 23 8 9
( ) ( ) 18 14 86 78
,
7 11 39 47
( ) ( )
−10 16 0 10
, ,
−20 18 −14 8
( ) ( ) 3 4 −15 48
,
−6 9 −72 57
⎛ ⎞
1
7 (a) ⎜−2
⎟
⎝ 1⎠
1
( ) 46 29
8
29 78
⎛ ⎞
37
9 (a) ⎝ 13⎠
−6
(d)
( ) 11
28
(b)
⎛
⎜
⎝
⎞
5
5
⎟
⎠
−2
1
⎛ ⎞
8
(b) ⎝36⎠
19
⎛ ⎞
31
(e) ⎜33
⎟
⎝38⎠
18
(c)
⎛ ⎞
10
⎝31⎠
18
TechnicalComputingExercises8.3
Technical computing languages such asMATLAB ® are
usuallydesigned to perform operationson scalars,
vectorandmatrices.However,ashasbeendemonstrated
in thischapter, different mathematical rules apply when
workingwith vectors and matrices.Consider the
followingquantities:
a = −2 (a scalar quantity)
b = 7 (a scalar quantity)
( ) 1 3
c = , (a 2 by2matrix)
2 4
( ) 5 7
d = , (a 2 by 2 matrix)
6 8
⎛ ⎞
1 4
e = ⎝2 5⎠, (a 3 by2matrix)
3 6
( ) 135
f = , (a 2 by3matrix)
246
Load these asvariables in atechnical computing
language and thenattempt to perform the following
calculations andanswer the questions.
1. Find the product ofthe scalarsaandb.Isthisa
valid calculation?
2. Find the product ofthe scalar aand the matrixc.Is
thiscalculation valid? Similarlyfindthe product of
the matrixcandscalara.Do these calculations
produce the same result?
3. Find the productsofthe matricescandd,that iscd
anddc. Are these calculations valid and dothey
produce the same result?
4. Find the productsofthe matriceseand f,that isef
and fe.Are these calculations valid and dothey
produce the same result?
5. Find the productsofthe matricesd ande,that isde
anded. Are these calculations valid and dothey
produce the same result?
6. Findc 2 .Isthiscalculation valid?
7. Finde 2 .Isthiscalculation valid?
Solutions
1 Yes, the calculation is valid. Itis ascalar multiplied
byascalar.InMATLAB ® :
a*b
ans = -14
2 Yes, the calculations are valid and produce the same
result.
a*c
ans =
-2 -6
-4 -8